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Proof step 3 from proof valid-group-nodes-prefixn-append-nonend (previous step)

⊦ valid-group-nodes ((n ≤ #(gndx + mkgnode(nd, m, boolvar, false) ') ⊃ firstn(n, gndx + mkgnode(nd, m, boolvar, false) ');gndx + mkgnode(nd, m, boolvar, false) ')) = valid-group-nodes(prefixn(n, gndx))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
⊦ valid-group-nodes((n ≤ # gndx + 1 ⊃ firstn(n, gndx + mkgnode(nd, m, boolvar, false) ');gndx + mkgnode(nd, m, boolvar, false) ')) = valid-group-nodes(prefixn(n, gndx))

Rule argument

Additional information

Used simplifier rules: a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ # gnd ' = 0 +1; (s)% ⊦ #(gndx + gndx0) = # gndx + # gndx0; (s)